derivative (3x^3+3)(x^4-3x)

Lösung

ableitung von

(3 x^{3} + 3) (x^{4} - 3 x)

21 x^{6} - 24 x^{3} - 9

Schritte zur Lösung

\frac{d}{d x} ((3 x^{3} + 3) (x^{4} - 3 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{3} + 3, g = x^{4} - 3 x

= \frac{d}{d x} (3 x^{3} + 3) (x^{4} - 3 x) + \frac{d}{d x} (x^{4} - 3 x) (3 x^{3} + 3)

\frac{d}{d x} (3 x^{3} + 3) = 9 x^{2}

\frac{d}{d x} (x^{4} - 3 x) = 4 x^{3} - 3

= 9 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (3 x^{3} + 3)

Vereinfache

9 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (3 x^{3} + 3) : 21 x^{6} - 24 x^{3} - 9

= 21 x^{6} - 24 x^{3} - 9

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